Add solution for Project Euler problem 102 (#4051)

* Added solution for Project Euler problem 102

* Got rid of map functions

* Snake case variable names

* Type hints

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

project_euler/problem_102/sol1.py

@@ -0,0 +1,81 @@
+"""
+Three distinct points are plotted at random on a Cartesian plane,
+for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
+
+Consider the following two triangles:
+
+A(-340,495), B(-153,-910), C(835,-947)
+
+X(-175,41), Y(-421,-714), Z(574,-645)
+
+It can be verified that triangle ABC contains the origin, whereas
+triangle XYZ does not.
+
+Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text
+file containing the coordinates of one thousand "random" triangles, find
+the number of triangles for which the interior contains the origin.
+
+NOTE: The first two examples in the file represent the triangles in the
+example given above.
+"""
+
+from pathlib import Path
+from typing import List, Tuple
+
+
+def vector_product(point1: Tuple[int, int], point2: Tuple[int, int]) -> int:
+    """
+    Return the 2-d vector product of two vectors.
+    >>> vector_product((1, 2), (-5, 0))
+    10
+    >>> vector_product((3, 1), (6, 10))
+    24
+    """
+    return point1[0] * point2[1] - point1[1] * point2[0]
+
+
+def contains_origin(x1: int, y1: int, x2: int, y2: int, x3: int, y3: int) -> bool:
+    """
+    Check if the triangle given by the points A(x1, y1), B(x2, y2), C(x3, y3)
+    contains the origin.
+    >>> contains_origin(-340, 495, -153, -910, 835, -947)
+    True
+    >>> contains_origin(-175, 41, -421, -714, 574, -645)
+    False
+    """
+    point_a: Tuple[int, int] = (x1, y1)
+    point_a_to_b: Tuple[int, int] = (x2 - x1, y2 - y1)
+    point_a_to_c: Tuple[int, int] = (x3 - x1, y3 - y1)
+    a: float = -vector_product(point_a, point_a_to_b) / vector_product(
+        point_a_to_c, point_a_to_b
+    )
+    b: float = +vector_product(point_a, point_a_to_c) / vector_product(
+        point_a_to_c, point_a_to_b
+    )
+
+    return a > 0 and b > 0 and a + b < 1
+
+
+def solution(filename: str = "p102_triangles.txt") -> int:
+    """
+    Find the number of triangles whose interior contains the origin.
+    >>> solution("test_triangles.txt")
+    1
+    """
+    data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
+
+    triangles: List[List[int]] = []
+    for line in data.strip().split("\n"):
+        triangles.append([int(number) for number in line.split(",")])
+
+    ret: int = 0
+    triangle: List[int]
+
+    for triangle in triangles:
+        ret += contains_origin(*triangle)
+
+    return ret
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

project_euler/problem_102/test_triangles.txt

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+-340,495,-153,-910,835,-947
+-175,41,-421,-714,574,-645